Re: Preventing LegendreP from self-extracting in manipulations
- To: mathgroup at smc.vnet.net
- Subject: [mg58051] Re: Preventing LegendreP from self-extracting in manipulations
- From: Scott Hemphill <hemphill at hemphills.net>
- Date: Fri, 17 Jun 2005 05:18:56 -0400 (EDT)
- References: <d893ok$svp$1@smc.vnet.net>
- Reply-to: hemphill at alumni.caltech.edu
- Sender: owner-wri-mathgroup at wolfram.com
"Vladislav" <kazimir04 at yahoo.co.uk> writes: > I have already tried to post the message, but it went lost. I repeat it > as a new therad. > > Can somebody help me with the following. I need present some functions > (prolate spheroidal functions) in the basis of the Legendre > polynomials. I.e. > I have functions like > > FF1 = 0.6 LegendreP[5, #1] + 0.7 LegendreP[6, #1] & > FF2 = 0.3 LegendreP[5, #1] + 0.2 LegendreP[6, #1] & > > I want to manipulate these functions and remain in the basis of prolate > functions. > For example I want to create a linear combination of functions, or > something like this. > > FF = .2FF1[#1] + .3FF2[#1] & > > It works well from the point of view of finding the numerical result, > but it do not give > the presentaion of the function in the basis of the Legendre > polynomials > > I would like to have create a function which would give the result like > > FFX = 0.9 LegendreP[5, #1] + 0.9 LegendreP[6, #1] &, so that I could > see the presentaion > of the function by typing FFX and obtaining 0.9 LegendreP[5, #1] + 0.9 > LegendreP[6, #1] &. > In practice these functions contain much more terms and having the form > like > 0.9 LegendreP[5, #1] + 0.9 LegendreP[6, #1] & is very important. In > the same way > I would not like to have the explicit presentation as plolinomials, > like -0.28125+ > 1.6875 w + 5.90625 w^2 + .. because of loss of accuracy for future > results. There are other ways to prevent loss of accuracy. Instead of "0.9" as a coefficient, use "9/10". Or if fractional arithmetic becomes too cumbersome, replace "0.9" with "N[9/10,32]" to specify extra precision. Were the suggestions made by the other posters sufficient? Scott -- Scott Hemphill hemphill at alumni.caltech.edu "This isn't flying. This is falling, with style." -- Buzz Lightyear